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Second-Order Time-Dependent Tangent Bundles and Geometric Mechanics

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Abstract

The aim of this paper is to geometrize time-dependent Lagrangian mechanics in a way that the framework of second-order tangent bundles plays an essential role. To this end, we first introduce the concepts of time-dependent connections and time-dependent semisprays on a manifold M and their induced vector bundle structures on the second-order time-dependent tangent bundle \(\mathbb {R}\times T^2M\). Then we turn our attention to regular time-dependent Lagrangians and their interaction with \(\mathbb {R}\times T^2M\) in different situations such as mechanical systems with potential fields, external forces and holonomic constraints. Finally, we propose some examples to support our theory.

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  1. Department of Mathematics, Faculty of Sciences, Bu-Ali Sina University, Hamedan, 65178, Iran

    Ali Suri

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  1. Ali Suri
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Correspondence to Ali Suri.

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Suri, A. Second-Order Time-Dependent Tangent Bundles and Geometric Mechanics . Mediterr. J. Math. 14, 154 (2017). https://doi.org/10.1007/s00009-017-0954-2

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  • DOI: https://doi.org/10.1007/s00009-017-0954-2

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